Ca hnk: The Calcium-rich Transient Supernova 2016hnk from a Helium Shell Detonation of a Sub-Chandrasekhar White Dwarf

SN 2016hnk was discovered by the Asteroid Terrestrial-impact Last Alert System (ATLAS; Tonry et al. 2018) on 2016 October 27 (MJD 57688) using the ACAM1 instrument with a cyan filter (Tonry et al. 2016). SN 2016hnk has a discovery apparent magnitude of 17.91 and is located at α =02^h13^m1663, δ = −07°39'4080. SN 2016hnk is located 14 east and 124 north of the nucleus of the SBa galaxy MCG-01-06-070. In this paper, we use the reported host-galaxy distance and redshift of 72.9 Mpc and 0.016268, respectively, in standard ΛCDM cosmology (H₀ = 70 km s⁻¹ Mpc⁻¹, Ω_M = 0.27, Ω_Λ = 0.63).

SN 2016hnk was first classified as a peculiar SN Ia by Cannizzaro et al. (2016) who noted its resemblance to SN 1991bg (91bg-like) near maximum light. The initial spectrum was described as being red, with the presence of strong Si ii λ6355, O i λ7774, and near-infrared Ca ii spectral features. Dimitriadis et al. (2016) made a similar classification and indicated the similarity of SN 2016hnk with SNe 1991bg and 1999by. Finally, the classification by Pan et al. (2016) illustrated a similarity between SN 2016hnk and the Ca-rich transient PTF09dav (Sullivan et al. 2011) given their similar colors, peak absolute magnitude, and spectral features. Pan et al. noted the distinct absorption profiles at 5350, 5540, and 7120 Å, which Sullivan et al. (2011) attributed to Sc ii (first two) and Ti ii (third). We discuss these specific spectral features in Section 4.2.

We imaged SN 2016hnk between 2016 November 1 and 2017 February 17 with the Direct camera on the Swope 1 m telescope at Las Campanas Observatory, Chile. Observations were performed in Johnson BV and Sloan ugri filters. We performed bias-subtraction and flat-fielding, stitching, registration, and photometric calibration using photpipe (Rest et al. 2005). For our photometric calibration, we used stars in the Pan-STARRS PS1 DR1 catalog (Flewelling et al. 2016) transformed from gri magnitudes to the uBVgri Swope natural system following the Supercal method (Scolnic et al. 2015). Difference imaging was performed using Swope BVgri and u templates obtained on 2017 November 15 and 2017 December 10, respectively. Final photometry was performed in the difference images with DoPhot (Schechter et al. 1993). A Swope Bri image of SN 2016hnk, mapped to RGB channels, from 2016 October 31, is shown in Figure 1.

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Additional imaging of SN 2016hnk was obtained by the Las Cumbres Observatory Global Telescope (LCOGT; Brown et al. 2013) and the Foundation Supernova Survey with Pan-STARRS (Foley et al. 2018). We performed a similar photometric reduction on the LCOGT data as the Swope imaging, which included standard subtractions and difference imaging. PS1 images of SN 2016hnk were reduced with the same custom-built pipeline as for the PS1 Medium Deep Field survey data. The basic data processing was performed by the PS1 Image Processing Pipeline (Magnier 2006; Magnier et al. 2013; Waters et al. 2016). Single-epoch images were then processed through a frame-subtraction analysis using photpipe, which determines an appropriate spatially varying convolution kernel using HOTPANTS (Becker 2015). After the convolutions were performed, the template image was subtracted from the survey image. Detections of significant flux excursions in the difference images were found using DoPHOT (Schechter et al. 1993).

SN 2016hnk has a reported Milky Way reddening and associated extinction of E(B − V) = 0.0224 mag and A_V = 0.069 mag (Schlegel et al. 1998; Schlafly & Finkbeiner 2011), respectively, which we correct for using a standard Fitzpatrick (1999) reddening law and R_V = 3.1. We do not correct for host-galaxy contamination given the absence of Na i D absorption in all spectra at the host redshift. We demonstrate the effect of further de-reddening in the color curves shown in Figure 7 and discuss the intrinsic color of SN 2016hnk in Section 6.1.

Galbany et al. (2019) report a host extinction of E(B − V) = 0.45 mag using the observed ratio of Hα and Hβ fluxes from host-galaxy spectra. However, because the exact vertical location of the source in the galaxy is unknown, Na i D absorption is the most accurate indicator of extinction at the site of the explosion. Thus all multi-color optical photometry of SN 2016hnk in Figure 2 has only been corrected for Milky Way extinction. All photometric observations are listed in Table A1.

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Final photometric observations of SN 2016hnk were obtained using the imaging camera on the Keck telescope Low-resolution Imaging Spectrometer (LRIS; Oke et al. 1995). The source was observed on 2017 July 20 in BR as well as on 2017 August 16 in BVRI. Observations were performed in the blue and red channels simultaneously with the B+R filters and V+I filters and the D560 dichroic, and reduced using photpipe. For our photometric calibration, we used secondary calibrators in each image with magnitudes derived from SDSS standard stars transformed to the BVRI system (Bilir et al. 2011; Alam et al. 2015). Keck BVRI templates were acquired on 2019 September 25 and image subtraction was performed using HOTPANTS. Final photometry was performed on the difference images using photpipe. The only late-time detection of SN 2016hnk was in the I-band at a phase of +291 days relative to maximum light. The I-band detection image is shown in Figure 1 and has an associated apparent magnitude of 23.57 ± 0.09 mag.

All recovered magnitudes in other Keck filters are reported as upper limits as shown in the full optical light curve in Figure 2 and listed in Table A1.

In Figure 3, we present optical spectral observations of SN 2016hnk from +1 to +264 days relative to B-band maximum. We first observed SN 2016hnk on 2016 October 30 with the Goodman High Throughput Spectrograph (Clemens et al. 2004) on the Southern Astrophysical Research Telescope (SOAR). SN 2016hnk was then observed using the Kitt Peak Ohio State Multi-object Spectrograph (KOSMOS; Martini et al. 2014) on 2016 November 30 and December 27 as well as with SOAR on 2017 January 3.

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For all spectral observations, standard CCD processing and spectrum extraction were accomplished with IRAF.¹⁴ The data were extracted using the optimal algorithm of Horne (1986). Low-order polynomial fits to calibration-lamp spectra were used to establish the wavelength scale, and small adjustments derived from night-sky lines in the object frames were applied. We employed our own IDL routines to flux calibrate the data and remove telluric lines using the well-exposed continua of the spectrophotometric standard stars (Wade & Horne 1988; Foley et al. 2003). Details of our spectroscopic reduction techniques are described in Silverman et al. (2012).

SN 2016hnk was last observed by Keck/LRIS on 2017 July 20. At this time the SN had faded significantly and was undetectable in guide camera images, and a blind offset from a nearby star was necessary to acquire the target. In the two-dimensional spectrogram, we did not detect continuum emission from the SN, but did see a broad absorption feature consistent with the wavelength of [Ca ii] λλ7291, 7324. Because of the bright and spatially varying background caused by the SN proximity to the center of its host galaxy, we chose to perform a two-dimensional background subtraction using a third-order Legendre polynomial in the spatial direction. Details of this method can be found in Foley et al. (2009b). While this method produced significantly better results than others attempted, there is still some residual continuum that we believe to be galactic emission.

Additional early-time spectral observations (+2 to 4 days after peak) were retrieved through the WISeREP archive¹⁵ (Yaron & Gal-Yam 2012) and are presented within the complete list of spectral observations in Table A2.

We fit a low-order polynomial to the SN 2016hnk light curve to find best-fit B- and r-band peak absolute magnitudes of M_B = −15.40 ± 0.088 at MJD 57690.2 ± 0.7 and M_r =−17.17 ± 0.04 at MJD 57693.3 ± 0.6, respectively. We calculate a Phillips (1993) decline parameter value of Δm₁₅(B) = 1.31 ± 0.085 mag from our B-band light-curve fits. All values are in agreement with those presented in G19.

Based on the ATLAS light curve, the last non-detections in ATLAS cyan and orange filters were at MJD 57667.56 and 57671.55, respectively, with the first detection being in ATLAS-o at MJD 57680.52. We can use these data to constrain the rise time if we match the ATLAS-o observations with all r-band data given the similarity in transmission functions of each filter. Consequently, the rise time of SN 2016hnk is in a range of 12.8 days < t_r < 21.8 days. We constrain the rise time further by showing that SN 2016hnk has a faster rise than the 17 days quoted for SN 2018byg (Figure 4(a)) and a similar rise to PTF11kmb (Figure 6(b)), which has t_r = 15 days (Lunnan et al. 2017). From this comparison, we estimate a rise time for SN 2016hnk of t_r = 15 ± 2 days.

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We present light-curve and spectral comparisons of SNe 2016hnk and 2018byg in Figure 4. In 4(a) we show the parallel between r- and g-band photometry for these objects. Both SNe exhibit a fast rise time of ⪅17 days, with SN 2016hnk having a slower decline in the r-band.

SN 2016hnk has a lower peak M_B than normal SNe Ia as well as sub-luminous SN Ia varieties such as SNe Iax, 91bg-like, and 02es-like objects. SN 2016hnk does have a similar Δm₁₅(B) to SNe Iax and SN 2002es, but it is significantly slower fading than other Ca-rich transients and 91bg-like objects. Δm₁₅(B) versus M_B comparison of these objects and SN 2016hnk is shown in Figure 5.

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We present light-curve comparisons of SN 2016hnk to peculiar thermonuclear SNe in Figure 6. As shown in Figures 6(a) and (b), SN 2016hnk is more luminous than Ca-rich transients SN 2005E (Perets et al. 2010), PTF 09dav (Sullivan et al. 2011), SN 2010et (Kasliwal et al. 2012), PTF11kmb (Gal-Yam et al. 2011), SN 2012hn (Valenti et al. 2014), PTF12bho (Kasliwal et al. 2012), and iPTF16hgs (De et al. 2018), in addition to having a slower decline rate. The rise time of these Ca-rich objects is faster than that observed in SN 2016hnk, the most similar objects being SN 2007ke and PTF11kmb, each having a rise time of 15 days (Kasliwal et al. 2012; Lunnan et al. 2017).

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Additionally, we present the absolute magnitude B-band light curves of the following SNe Ia with respect to SN 2016hnk: SN 1991bg (Filippenko et al. 1992; Leibundgut et al. 1993), SN 1991by (Garnavich et al. 2004), SN 2002es (Ganeshalingam et al. 2012), SN 2005ke (Gal-Yam 2005), SN 2011fe (Li et al. 2011; Nugent et al. 2011), and SN 2012Z (McCully et al. 2014; Stritzinger et al. 2015). In addition to a difference in peak magnitude, the B-band decline of SN 2016hnk after 20 days is unlike that of normal/sub-luminous SNe Ia or SNe Iax. G19 propose that this late-time light-curve excess could be the result of either a light echo or intervening interstellar material dust at ≈1 pc from the explosion site. However, G19 show that there is no evidence of a light echo in SN 2016hnk spectra and the lack of significant changes to the r − i color evolution at these times also disfavors this scenario.

In Figure 7, we present B − V , g − r, and r − i color comparison plots for SN 2016hnk, Ca-rich transients, and SNe Ia sub-classes. In Figure 7(a), SN 2016hnk's B − V colors are generally redder than all other varieties of normal and sub-luminous SNe Ia as well as SNe Iax. In relation to SNe Ia, SN 2016hnk's g − r and r − i color evolution is also significantly different: SN 2016hnk is ≈0.3–0.6 mag redder in g − r and ≈0.25–0.5 mag bluer in r − i than even the most similar sub-luminous SNe Ia. Additionally, we present g − r and r − i colors of SN 2018byg as light blue stars in Figures 7(b) and (d). The color evolution of SN 2016hnk is consistent with SN 2018byg to within 0.5 mag in r − i and g − r. However, SN 2018byg is slightly redder at most epochs. Comparing to Ca-rich objects, SN 2016hnk is consistent to within 0.2 mag in g − r colors, but is ≈0.5 mag bluer than the typical Ca-rich object in r − i. As shown by the pink squares in Figure 7, if there were dust reddening from the host galaxy, SN 2016hnk would be even bluer in r − i, making it an exceptionally odd object.

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We construct a pseudo-bolometric light curve for SN 2016hnk using a combination of multi-color optical photometry from Swope, PS1, and LCOGT observations. Luminosities are calculated by trapezoidal integration of SN flux in BVgriz filters (3000–9000 Å). In regions without complete color information, we extrapolate between light-curve data points using a low-order polynomial spline. We present the early-time, pseudo-bolometric light curve in Figure 8(a). For reference, we display models from the Heidelberg Supernova Model Archive¹⁶ that include various binary configurations and explosion mechanisms. We also include an estimated pre-maximum bolometric luminosity at −9.5 days by integrating the pre-maximum brightness spectra of SN 2016hnk and a similar object, SN 2018byg. These spectra are scaled to the first ATLAs-o detection and each phase is relative to r-band peak brightness.

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Using the constructed light curve, we find a peak luminosity of (8.5 ± 0.5) × 10⁴¹ erg s⁻¹. This value is smaller than that calculated in G19 who apply a significant host-galaxy reddening correction. We, however, do not apply such a correction because we find no evidence for host extinction (see Section 2.2). We can then use L_bol at peak to estimate the total mass of synthesized ⁵⁶Ni, M_Ni, assuming that the radiated luminosity is generated via thermalization of γ-rays from the β-decay of ⁵⁶Ni $\to$ ⁵⁶Co (Arnett 1982). We use the following relation to calculate ⁵⁶Ni mass:

$$\begin{eqnarray}&&{M}_{\mathrm{Ni}}=\displaystyle \frac{{L}_{\mathrm{bol}}}{\gamma \dot{S}({\tau }_{{\rm{r}}})}\end{eqnarray} \tag{ 1 }$$

where τ_r is the rise time and γ is the ratio of bolometric to radioactivity luminosities. As in Nugent et al. (1995), we adopt γ = 1.2 ± 0.2. $\dot{S}$ is the radioactivity luminosity per solar mass of ⁵⁶Ni decay:

$$\begin{eqnarray}\begin{array}{rcl}\dot{S} & = & \left(6.31{e}^{-{\tau }_{{\rm{r}}}/8.8\mathrm{days}}+1.43{e}^{-{\tau }_{{\rm{r}}}/111\mathrm{days}}\right)\\ & & \times {10}^{43}\ \mathrm{erg}\ {{\rm{s}}}^{-1}\ {M}_{\odot }^{-1}.\end{array}\end{eqnarray} \tag{ 2 }$$

Using τ_r = 15 ± 2 days (Section 3.1), we calculate M_Ni = 0.03 ± 0.01 M_⊙. This value is consistent to 1σ with that reported for PTF09dav (0.019 ± 0.003 M_⊙; Sullivan et al. 2011) and consistent to ∼2σ with the lowest-luminosity 91bg-like object, SN 2007ax (0.038 ± 0.008 M_⊙). The total ⁵⁶Ni mass mass in SN 2016hnk is also lower than that found for SN 2018byg (≈0.11 ${M}_{\odot }$; De et al. 2019), which is consistent with the observed difference in luminosity between the two objects at peak. The total ⁵⁶Ni mass in SN 2016hnk is still significantly less than the majority of sub-luminous SNe Ia.

We then use the relation from Foley et al. (2009a) to estimate the ejecta mass of SN 2016hnk:

$$\begin{eqnarray}&&{M}_{\mathrm{ej}}=0.16{\left(\displaystyle \frac{{\tau }_{{\rm{r}}}}{10\mathrm{days}}\right)}^{2}\left(\displaystyle \frac{0.1\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}}{\kappa }\right)\left(\displaystyle \frac{v}{2\times {10}^{8}\,\mathrm{cm}\,{{\rm{s}}}^{-1}}\right)\end{eqnarray} \tag{ 3 }$$

where κ is the opacity and v is the ejecta velocity. Using a standard SN Ia opacity of 0.2 cm²g⁻¹ and a calculated ejecta velocity of −10,300 $\mathrm{km}\,{{\rm{s}}}^{-1}$ from Si ii absorption, we find M_ej = 0.9 ± 0.3 ${M}_{\odot }$. Given the strength of Ca ii in the SN 2016hnk spectra, the true opacity could be larger than a normal SN Ia, which in turn would yield a smaller ejecta mass than our current estimate.

We also examine the decline of the pseudo-bolometric light curve at late times to check the consistency with standard ⁵⁶Co decay. As shown in Figure 8(b), the lack of multi-filter photometric data after ∼100 days makes it difficult to calculate precise late-time bolometric luminosities for SN 2016hnk. However, we can place an estimate on the bolometric luminosity by scaling nebular spectra of SN 2016hnk and similar objects to the Keck I-band flux at +291 days. If we first assume that all the flux at late times is derived from [Ca ii] emission, we can scale the Keck LRIS spectrum at +264 days to the I-band flux and integrate over the wavelength range of the Keck I-band transmission function. With this method, we calculate a luminosity of 2.2 ± 0.90 × 10³⁹ erg s⁻¹ (red star in Figure 8(b)). The phase of the Keck spectrum and the I-band detection are not identical, but this does not add extra uncertainty on the luminosity if we assume that the spectral evolution between epochs is small. Additional uncertainties on this measurement originate from the lack of photometric detections in other Keck filters; this may indicate additional flux outside of the I-band transmission curve. However, we consider this unlikely given that the only detectable feature in the Keck spectrum is [Ca ii]. We place additional constraints on SN 2016hnk's bolometric decline by estimating its luminosity using SNe Iax 2002cx and 2008A, which have a similar Ca-dominated spectral composition at nebular times. Scaling the spectra of these objects at a similar phase to the Keck I-band flux, we calculate additional bolometric luminosities for SN 2016hnk. Luminosities from 2002cx and 2008A SEDs are within the errorbars present in 8(b).

We then use our estimates for the late-time bolometric luminosity of SN 2016hnk to explore the standard ⁵⁶Ni-powered decline that is typically observed in SNe Ia. As shown in Figure 8(b), the bolometric decline of SN 2016hnk is slower than that of SN 2011fe (black; Zhang et al. 2016) and SN 1991bg (cyan; Stritzinger et al. 2006). The SN 2016hnk decline rate is also inconsistent with a simple ⁵⁶Co $\to$ ⁵⁶Fe decay (i.e., complete γ-ray trapping) as presented by the dashed blue line in 8(b).

We model the radioactive decay-powered light curve using a similar method to late-time studies of SNe Ia (Seitenzahl et al. 2013; Graur et al. 2016; Dimitriadis et al. 2017; Shappee et al. 2017; Jacobson-Galán et al. 2018). We employ the Bateman equation to fit the bolometric decline produced by radioactive isotopes:

$$\begin{eqnarray}\begin{array}{rcl}{L}_{A}(t) & = & 2.221\displaystyle \frac{{\lambda }_{A}}{A}\displaystyle \frac{M(A)}{{M}_{\odot }}\displaystyle \frac{{q}_{A}^{x}+{q}_{A}^{l}{f}_{A}^{l}(t)+{q}_{A}^{\gamma }{f}_{A}^{\gamma }(t)}{\mathrm{keV}}\\ & & \times \ \exp (-{\lambda }_{A}t)\times {10}^{43}\ \mathrm{erg}\ {{\rm{s}}}^{-1}\end{array}\end{eqnarray} \tag{ 4 }$$

where t is time since explosion, λ_A is the decay constant, A is the atomic number, and q^l, q^γ, and q^x are the average energies of charged leptons, γ-rays, and X-rays, respectively, per decay. All decay energies and constants are as presented in Table 2 of Seitenzahl et al. (2014). We assume complete trapping of energy deposited by charged leptons (i.e., ${f}_{A}^{l}$ = 0) and do not include X-ray energies in our fits. We use the following expression for γ-ray trapping:

$$\begin{eqnarray}&&{f}_{A}^{\gamma }=1-\exp \left[-{\left(\displaystyle \frac{{t}_{A}^{\gamma }}{t}\right)}^{2}\right]\end{eqnarray} \tag{ 5 }$$

where ${t}_{A}^{\gamma }$ is the γ-ray trapping timescale for a given radioactive isotope produced in the explosion (Woosley et al. 1989; Seitenzahl et al. 2014).

In our model, we fit for the mass and γ-ray trapping timescale of ⁵⁶Co as well as the mass of ⁵⁷Co. However, the luminosity contribution is dominated by synthesized ⁵⁶Co until ≈300 days after explosion, thus making the ⁵⁷Co contribution negligible on this timescale. Modeling the data with Equation (4), we find ⁵⁶Co and ⁵⁷Co masses of 0.029 ± 0.001 and ≈0 ${M}_{\odot }$, respectively. This result is consistent with our total ⁵⁶Ni mass estimate of M_Ni = 0.03 ± 0.006 M_⊙. We also calculate a trapping timescale of ${t}_{56}^{\gamma }={60.06}_{-3.71}^{+4.12}$ days. We display our model fit as the dashed magenta line in Figure 8(b).

We model the early-time spectra of SN 2016hnk with the spectral synthesis code SYNAPPS (Thomas et al. 2011) in order to understand the elements produced in the explosion. SYNAPPS is utilized primarily for line identification and relies on generalized assumptions about the SN such as spherical symmetry, local thermal equilibrium (LTE), and homologous expansion of ejecta. As shown in Figure 9(a), we identify the following species most commonly found in thermonuclear SNe: O i, Si ii, S ii, Ca ii, Ti ii, Fe ii/iii, and Co i/ii. We do not detect C i nor Mg i in our fits and the detection of Na i is probable but not definite. We also find no detectable He i in any SYNAPPS modeled spectra. This finding is unlike other Ca-rich objects, which typically show clear signatures of photospheric helium near peak.

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We ran various SYNAPPS fits in an attempt to identify more exotic elements such as Cr ii, Sc ii, and Sr ii, all of which are claimed to be robustly detected in SYNAPPS models of PTF09dav by Sullivan et al. (2011). We present a model comparison in Figure 9(b) of a fit including typical thermonuclear species (e.g., Fe ii/iii, Ti ii, Co i/ii; (blue line)) and a fit with both typical species (e.g., Fe ii/iii and Ti ii; (red line)) in additional to exotic species (e.g., Cr ii and Sc ii). The two line profiles at λλ5400, 5550 are more accurately fit with blends of S ii and Fe-group elements than Sc ii. We also find that adding Cr ii does not improve our SYNAPPS fits. Despite the visual similarities between near-peak spectra of SN 2016hnk and PTF09dav, we cannot place the same level of confidence on the detection of Sc ii, Cr ii, and Sr ii in SN 2016hnk as Sullivan et al. (2011) did for PTF09dav.

SN 2016hnk is extremely similar to SN 2018byg at each phase of spectroscopic observations presented in 4(b). At similar phases near maximum light, both objects contain broad, high-velocity Ca ii absorption features with velocities of −17151.41 ± 540.10 $\mathrm{km}\,{{\rm{s}}}^{-1}$ in SN 2016hnk and −22221.70 ± 706.0 $\mathrm{km}\,{{\rm{s}}}^{-1}$ in SN 2018byg. Ca ii and Si ii velocities were calculated by fitting the minimum of each absorption feature using a low-order polynomial. A more complete velocity evolution for both objects is presented in Figure 18. Furthermore, the spectra of SNe 2016hnk and 2018byg both show suppressed emission from line blanketing of Fe-group elements. As indicated by the colors shown in Figure 7, SN 2016hnk's "redder" B − V colors with respect to its "bluer" r − i colors are the result of this blueward line blanketing. This characteristic is unique to these two SNe and sets them apart from other sub-luminous thermonuclear objects such as 91bg-like objects (Figure 10).

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Spectroscopic differences between the two objects include higher overall elemental velocities in SN 2018byg and deeper Si ii/O i absorption in SN 2016hnk. There are no published nebular spectra of SN 2018byg to compare with our late-time SN 2016hnk spectral observations.

Initial spectral classifications of SN 2016hnk noted similarities between both sub-luminous, 91bg-like objects as well as the Ca-rich transient PTF09dav. We show a time-series spectral comparison in Figure 11. As shown in Figure 11(a), SN 2016hnk has matching Si ii, O i, and Ca ii absorption to 91bg- and 02es-like objects. Similar features are also observed in PTF09dav, but with slower expansion velocities than those in the SN 2016hnk spectra. Fe ii/iii emission and Ti ii absorption profiles are shared between both objects. SN 2016hnk, however, has significantly suppressed emission in blue wavelengths compared to PTF09dav.

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The primary differences between SN 2016hnk and other sub-luminous SNe Ia are the relative velocities and the prominence of Fe-group elements. While the Si ii velocity of SN 2016hnk does match 91bg-like objects, the Ca ii in SN 2016hnk is moving ∼7000 $\mathrm{km}\,{{\rm{s}}}^{-1}$ faster than the velocities observed in "91bg-like" SNe 1991bg (10350 ±380 $\mathrm{km}\,{{\rm{s}}}^{-1}$), 1999 by (9290 ± 450 $\mathrm{km}\,{{\rm{s}}}^{-1}$), and 2005ke (11100 ± 680 $\mathrm{km}\,{{\rm{s}}}^{-1}$) near peak. This variation in Ca ii velocity suggests a different explosion mechanism for SN 2016hnk than that of 91bg-like objects. Furthermore, at early times, the observed line blanketing of Fe-group elements in the SN 2016hnk spectra is not observed in other comparison objects presented in Figure 11(a).

Despite the similar prevalence of [Ca ii] lines in the nebular phase, the dominance of Fe-group elements in 91bg-like objects is not observed in the Keck spectrum of SN 2016hnk at +264 days. As shown in Figure 11(c), the nebular spectra of all 91bg-like objects have prominent [Fe ii], [Fe iii], and [Co ii] emission features in blue wavelengths. These features are not present in the SN 2016hnk spectrum at a similar phase, which suggests that significantly less ⁵⁶Ni was synthesized during explosion. This observed contrast is supported by SN 2016hnk's low peak luminosity as compared to other sub-luminous SN Ia varieties. Furthermore, the [Ca ii] profile in SN 2016hnk is much narrower than that shown in the 91bg-like objects, all of which possess a blend of [Ca ii] and [Ni ii] emission at ∼7300 Å.

Nebular spectra of SN 2016hnk does show some similarities to observations of other Ca-rich objects at late times. In Figure 12, we present SN 2016hnk spectra at +66 days and +264 days in relation to most nebular spectra of Ca-rich transients. There is a noticeable parallel between the [Ca ii] emission features in all presented objects, in addition to the minor or non-existent presence of Fe-group elements. [Ca ii] line profiles are similar in all objects and do not show significant [Ni ii] line blending. Like PTF09dav, SN 2016hnk does not have detectable [O i] and is thus significantly more O-poor than other objects such as 2003dr, 2005E, PTF11kmb, and 2012hn. We present direct comparison of [O i] and [Ca ii] line profiles in Figure 13(a). Furthermore, SN 2016hnk does not show narrow Hα emission at late times as is detected in PTF09dav.

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We compare the [Ca ii]/[O i] ratio of SN 2016hnk to all Ca-rich objects and Type Ibc/IIP/IIb SNe in 13(b). Given the lack of observed [O i] in both objects, PTF09dav and SN 2016hnk have the highest [Ca ii]/[O i] ratio with respect to other SNe. This indicates a relatively O-poor explosion for both PTF09dav and SN 2016hnk as compared to most other Ca-rich objects.

These spectroscopic comparisons have demonstrated that SN 2016hnk is most similar to SN 2018byg given its observed blueward line blanketing and its strong, high-velocity Ca ii features. SN 2016hnk has some similar line profiles to 91bg-like SNe (e.g., Si ii and S ii), but has significantly faster Ca ii velocities and substantial line blanketing than this sub-class of SNe Ia. SN 2016hnk also has weaker Fe-line transitions than these objects at nebular times. Like other Ca-rich transients, the nebular spectra of SN 2016hnk is dominated by [Ca ii] emission. While the ratio of [Ca ii]/[O i] line fluxes for Ca-rich transients is typically greater than 2, this ratio for SN 2016hnk and PTF09dav is almost twice that of typical Ca-rich objects. This suggests either stronger calcium emission in SN 2016hnk or a limited oxygen presence in this SN than Ca-rich SNe.

As shown in Figure 14, SN 2016hnk's [Ca ii] emission profile is quite similar to that found in nebular phase spectra of SNe Iax. Also "Ca-rich" at late times, SNe Iax exhibit strong [Ca ii] and variable [Fe ii]/[Ni ii] emission features, both of which are tracers of initial WD mass and the possible wind from a bound SN remnant (Foley et al. 2016). Unlike most SNe Iax, SN 2016hnk does not have visible [Ni ii] emission, which suggests that there are very few stable nickel isotopes, such as ⁵⁸Ni, present in the ejecta. This is indicative of a sub-Chandrasekhar explosion in which the WD density is too low for sufficient electron capture. This conclusion is supported by our ejecta mass estimate of ∼0.9 ${M}_{\odot }$ (Section 3.2). Furthermore, as shown in Foley et al. (2016), narrow forbidden lines in nebular spectra may result from wind from a bound remnant. Such a model could be a viable explanation for SN 2016hnk at late times given its [Ca ii] profile shape is consistent with SNe Iax such as 2008A and 2010ae.

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The single-degenerate (SD) progenitor channel involves a WD in a binary system with a non-degenerate companion star. In this scenario, it is predicted that ablated H- or He-rich material from the non-degenerate companion will be swept up by the SN ejecta and should be detectable in late-time spectra as narrow emission lines with velocities of ≈1000 $\mathrm{km}\,{{\rm{s}}}^{-1}$ (Marietta et al. 2000; Mattila et al. 2005; Liu et al. 2012, 2013a; Pan et al. 2012; Lundqvist et al. 2013). We test this scenario by calculating upper limits on the mass of stripped hydrogen and helium potentially present in the nebular spectrum of SN 2016hnk.

We preface this analysis by stating that all stripped mass models used have been designed specifically for SNe Ia and not Ca-rich or low-luminosity thermonuclear objects. Thus these models are most notably different from SN 2016hnk in their energetics and total Ni mass produced, in addition to possible asymmetries. Consequently, the lower overall energies and SN densities in Ca-rich objects may affect the mixing of H/He circumstellar material, but the differences in Ni mass between each SN type will scale with the luminosity. Nonetheless, these models and radiative transfer simulations are applicable to this analysis as a means of testing an SD companion interaction scenario for SN 2016hnk.

We visually examine the +264 day nebular spectrum of SN 2016hnk and find no obvious detections of narrow Hα or He i emission. We do, however, observe a narrow feature near λ6563 in the nebular spectrum, which has a FWHM velocity of 203.65 ± 55.8 $\mathrm{km}\,{{\rm{s}}}^{-1}$. This velocity is low for SN-related material, e.g., the Hα emission in PTF09dav has a velocity of 1315.17 ± 241.05 $\mathrm{km}\,{{\rm{s}}}^{-1}$. Furthermore, this feature does not have significant signal-to-noise ratio compared to the overall spectral noise. Therefore we perform the analysis of potential ablated material by assuming a non-detection of nebular Hα emission.

To calculate the stripped hydrogen luminosity limit, we simulate a marginal detection by modeling the Hα emission as a Gaussian profile (FWHM = 1000 $\mathrm{km}\,{{\rm{s}}}^{-1}$) with a peak flux of three times the spectrum's root mean square (rms) flux (Sand et al. 2018; Dimitriadis et al. 2019). We present the simulated limit for marginal detection of Hα emission in Figure 15(a).

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We use the 3σ flux limit for marginal detection to calculate the luminosity limit of stripped hydrogen in the nebular spectrum. We then convert the Hα luminosity to stripped mass using the following relation from Botyánszki et al. (2018):

$$\begin{eqnarray}&&{\mathrm{log}}_{10}({L}_{{\rm{H}}\alpha })=-0.2{M}_{1}^{2}+0.17{M}_{1}+40,\end{eqnarray} \tag{ 6 }$$

where L_Hα is the Hα luminosity in cgs units at 200 days after peak, ${M}_{1}={\mathrm{log}}_{10}({M}_{{\rm{H}}}/{M}_{\odot })$, and M_H is the stripped hydrogen mass. We re-scale our estimated Hα luminosity limit because this relation is derived at exactly 200 days after peak. We calculate the decline in luminosity of SN 2016hnk to be a factor of 4 between 200 and 300 days. We find a Hα luminosity limit luminosity limit of L_Hα < 1.3 × 10³⁸ erg s⁻¹, which corresponds to 4.6 × 10⁻³ ${M}_{\odot }$ of undetected, stripped H-rich material in SN 2016hnk. This mass is an order of magnitude lower than model predictions for stripped H-rich material that is swept-up by an SN Ia in a Roche-lobe-filling progenitor system (1.4 × 10⁻² to 0.25 ${M}_{\odot }$; Liu et al. 2012; Pan et al. 2012; Boehner et al. 2017).

To calculate the limit of stripped helium in SN 2016hnk, we mimic the procedure outlined in Jacobson-Galán et al. (2019) for He i λ6678. Our marginal detection calculation follows the same procedure as Hα and we display the 3σ limit for He i emission in Figure 15(b). As shown in Figure 4 of Botyánszki et al. (2018), the MS38 model produces an Hα emission line that is ∼5 times more luminous than He i λ6678. Because of this, we modify Equation (6) to have the following form:

$$\begin{eqnarray}&&{\mathrm{log}}_{10}({L}_{\mathrm{He}})=-0.2{M}_{1}^{2}+0.17{M}_{1}+39.3,\end{eqnarray} \tag{ 7 }$$

where ${M}_{1}={\mathrm{log}}_{10}({M}_{\mathrm{He}}/{M}_{\odot })$ and M_He is the stripped helium mass. We calculate a stripped helium luminosity limit of L_He < 6.8 × 10³⁷ erg s⁻¹ and a corresponding maximum stripped mass of 1.2 × 10⁻² ${M}_{\odot }$ found using Equation (7). In SD He-star companion interaction models, the predicted ranges of stripped He-rich masses are 2.5 × 10⁻³−1.3 × 10⁻² ${M}_{\odot }$ (Pan et al. 2012) and 9.5 × 10⁻³−2.8 × 10⁻² ${M}_{\odot }$ (Liu et al. 2013b), both of which are consistent with the helium mass limit of SN 2016hnk.

The observed color evolution shows that SN 2016hnk is a highly reddened object. Currently, there is an established link between dust reddening and the strength of Na i D absorption for Milky Way stars and extragalactic SNe (Phillips et al. 2013). The lack of Na i D absorption in SN 2016hnk is a strong indication that the SN is unaffected by host reddening and that its red colors are intrinsic to the explosion. We further demonstrate this fact by de-reddening SN 2016hnk's color evolution. As shown in Figure 7(a), we de-redden B − V colors to match the bluest SNe Ia. Assuming a Fitzpatrick (1999) reddening law, this corresponds to an E(B − V) = 0.45 mag, which is the same as the host galaxy extinction reported in G19. While this shift does make the g − r colors more consistent with other objects, de-reddening the SN 2016hnk photometry causes the r − i color evolution to be even more inconsistent with SNe Ia. Therefore, if SN 2016hnk has a host-galaxy reddening of E(B − V) = 0.45 mag, then it would be ≥0.20 mag intrinsically bluer than all other SNe Ia, including those similar to SN 1991bg, in r − i. While possible, this scenario requires both a relatively large dust reddening with no Na D absorption, in contrast to other SNe with similar reddening, and intrinsically peculiar colors. Our preferred scenario of minimal reddening and intrinsically peculiar colors requires less exceptional circumstances. Furthermore, a single-explosion model can explain the peculiar colors, luminosity, and spectral evolution of SN 2016hnk.

SN 2016hnk's red colors can be explained by the helium shell double-detonation model proposed for this object. As shown in Section 5, the detonation of a helium shell on the surface of a C/O WD will pollute the outer layers of ejecta with Fe-group elements, which will suppress blueward flux. The products of the helium shell detonation will produce ashes that will cause the SN to have redder colors throughout its evolution, as observed in SN 2016hnk. Thus we attribute the observed red colors of SN 2016hnk to a helium shell detonation, which we show to be consistent with observations of this event in Figures 16 and 17.

The challenge in modeling SN 2016hnk lies in the lack of early-time data. The typical approach is to constrain the model parameters solely with photometry. The magnitude of the early flux excess constrains the mass of the helium shell, and peak magnitude reflects the total mass of the progenitor star. We would then compare the spectra and see if the event is consistent with a double-detonation explosion. This method was used for SN 2018byg by De et al. (2019). However, in the case of 2016hnk, we can only constrain the total mass (or equivalently a ⁵⁶Ni mass) from the peak luminosity, and we estimate the mass of the helium shell by examining the synthetic spectra at the time of peak brightness. When we examine the line-blanketed part of the spectrum (λ < 5000 Å) we find a good agreement with the 0.02 ${M}_{\odot }$ helium shell.

Another source of possible concern is the poor fit of our model to the slow decline of 2016hnk (Figure 16). This might be the result of the LTE approximation in the radiative transport calculations, which underpredict the flux once the ejecta becomes optically thin. This occurs ∼30–40 days after explosion for sub-Chandrasekhar mass models. Future non-LTE modeling is required to understand if the slow decline of SN 2016hnk can be modeled with a double-detonation explosion of this total mass of 0.87 ${M}_{\odot }$ or if the slow decline requires a more massive ejecta to account for the required diffusion time as, suggested in G19. However, an alternative explanation for this light-curve plateau is the emergence of blueward flux that was previous suppressed by Fe-group elements in the outer ejecta. This would occur once the outer ejecta expands and becomes optically thin, thus causing an increase in flux in the bands affected by early-time line blanketing (e.g., u, B, g, V bands). This scenario seems plausible based on the spectral evolution after t ∼ 20 days in both our data set and in G19, but a more robust analysis of spectral color evolution would need to be done to verify this model.

Our observational inferences on SN 2016hnk are similar to those presented in G19. We both find SN 2016hnk to be a peculiar thermonuclear object with a low overall luminosity and observed red colors. We obtain similar values for Δm₁₅(B) and M_B at peak, both of which are dissimilar from those found in SNe Ia sub-classes. Additionally, both of our observations have shown SN 2016hnk to be rich in high-velocity calcium, which dominates the nebular spectrum as [Ca ii] emission. We furthermore agree that exotic elements such as Sc ii, Cr ii, and Sr ii are most likely not found within the SN 2016hnk photospheric spectra. Despite its spectral similarity to PTF09dav, we find that blueward line profiles can be effectively modeled with Fe, Co, and Ti ions, similar to those found in G19. We also acknowledge the similarities between SN 2016hnk and 91bg-like peak spectra, as shown in G19. The closest matching spectral features are in the 5000–6300 Å  wavelength range, which includes similar Si ii absorption profiles in both objects (Figure 11(a)).

However, additional observations and modeling presented in this paper lead to a different overall interpretation than G19 on the intrinsic nature of SN 2016hnk. The observed rise time and velocities, in addition to consistency with shell models, demonstrate that SN 2016hnk produced 0.9 ${M}_{\odot }$ of ejecta, thus making it a sub-Chandrasekhar mass explosion. This SN was extremely Fe-poor, as shown by its low total Ni-mass and lack of Fe-group ions in its nebular spectra (Sections 3.2 and 4.2). As discussed in Section 6.1, the highly reddened colors are intrinsic to SNe and require an explosion mechanism to suppress blueward flux as shown in photospheric spectra. Consequently, we attribute these observed characteristics to a helium shell double-detonation of a sub-Chandrasekhar mass C/O WD.

In this paper we have demonstrated the physical differences between SN 2016hnk and 91bg-like objects. First, SN 2016hnk produced a small amount of Fe-group elements relative to 91bg-like events. This is demonstrated by the low inferred Ni-mass and lack of visible Fe-group elements in late-time spectra. Furthermore, as illustrated in Figure 5, SN 2016hnk has very different M_B versus Δm₁₅(B) measurement relative to 91bg-like events. The intrinsic color evolution of SN 2016hnk is also unlike any sub-luminous SN Ia; the SN's highly reddened B − V colors, in addition to "bluer" r − i, are inconsistent with other events (Figure 7). Additionally, the barred spiral host galaxy of SN 2016hnk may indicate a distinct stellar progenitor system from 91bg-like objects, which are typically found in elliptical galaxies with older stellar populations (van den Bergh et al. 2005; however, see Höflich et al. 2002; Garnavich et al. 2004). Conversely, if SN 2016hnk does in fact belong to the 91bg-like sub-class, it is the most extreme example yet observed.

The properties of SN 2016hnk challenge the traditional classification schemes of both sub-luminous SNe Ia and Ca-rich transients. Upon discovery, SN 2016hnk was classified as a 91bg-like object because of its spectral features and low luminosity. However, its prominent Ca ii features and "gap" absolute magnitude placed the SN in Ca-rich class. Its spectroscopic similarity to PTF09dav around maximum light also made the Ca-rich classification plausible. The Ca-rich distinction was later confirmed by its pre-nebular and nebular spectra, which were dominated by [Ca ii] emission in addition to having an integrated [Ca ii]/[O i] flux ratio greater than 2.

The ambiguity of SN 2016hnk's classification points to a need for diligence in understanding the similarities between low-luminosity thermonuclear objects. While it is true that SN 2016hnk shows some spectroscopic similarities to 91bg-like objects near peak, there are prominent physical differences that set these objects apart. Like Ca-rich events, SN 2016hnk was significantly more Fe-poor than any 91bg-like object yet observed. This became most apparent in nebular spectra and may be an indication that some 91bg-like or sub-luminous SNe Ia are mis-classified. There could be a number of sub-luminous SN Ia that are classified as such using maximum light spectra, but more physically resemble a "16hnk-like" or Ca-rich event. This is further supported by the limited number of sub-luminous objects that are tracked out to nebular times.

The color evolution of SN 2016hnk was essential in determining physical distinctions between the SN and sub-luminous SNe Ia. We emphasize the need for multi-band color information in order to understand how highly reddened, 16hnk-like SNe might compare to the larger thermonuclear sample. Furthermore, high-cadence color evolution could help to identify more than examples of thin shell detonations of sub-Chandrasekhar mass WDs.

As shown in De et al. (2019), SN 2018byg was thought to be a relatively rare event. Due to the observational similarity and consistent explosion models between both objects, we may initially conclude that SN 2016hnk was also a rare event with respect to thermonuclear SNe. This indicates that there are physical distinctions between the helium shell detonations that can explain SNe 2016hnk and 2018byg, in addition to models that have been shown to reproduce normal and sub-luminous SNe Ia (e.g., Shen et al. 2018; Polin et al. 2019a; Townsley et al. 2019). The thin shell detonation models that best matched these two SNe were distinct in their production of suppressed blueward flux, Fe-group line blanketing, high (>18,000 $\mathrm{km}\,{{\rm{s}}}^{-1}$) Ca ii velocities, and an intrinsically red color evolution. These physical properties can thus be applied as tracers for identifying more events like the apparent helium shell detonations that well explain SNe 2016hnk and 2018byg.

Furthermore, it may be possible that many Ca-rich events are caused by variations on the helium shell double-detonation model. A similar model was invoked to explain SN 2005E and it may be the case that other Ca-rich events could now be explained with new varieties of helium shell detonations. These events have noticeable similarities to this model such as low luminosities, reddened colors, dominant [Ca ii] emission at nebular times, and rapidly evolving light curves. Additionally, iPTF16hgs has a double-peaked light curve, which may be matched to the first ⁴⁸Cr peak produced in helium shell models. However, this explosion scenario needs to explain the He i observations in many Ca-rich objects; such an observation may require a fine-tuning of helium detonation on the WD surface in order to allow for sufficient amounts of un-burned helium to remain in the SN ejecta. Nonetheless, the observed Hα emission in PTF09dav poses a serious problem for this model since no hydrogen is produced in such an explosion.